444 
MEMOIR ON THE RESULTANT OF A SYSTEM OF TWO EQUATIONS. [148 
which may be developed in the form 
+12 . 345} 
-13 . 245} 
+ 14 . 235) 
+ 23 . 145] 
-15 . 234) 
- 24 . 135] 
+ 25 . 134) 
+ 34 . 125] 
-35 . 124} 
+ 45 . 123} 
where 12, 13, &c. are the terms of 
( a, b, c, d ) 
a, b, c, d 
and 123, &c. are the terms of 
( p, q, r ) 
p, q, r 
V, q, r 
viz. 12 is the determinant formed with the first and second columns of the upper 
matrix, 123 is the determinant formed with the first, second and third columns of 
the lower matrix, and in like manner for the analogous symbols. These determinants 
must be first calculated, and the remainder of the calculation may then be arranged 
as follows:—